Scientists fold origami into search for solutions

Laser physicist Robert J. Lang says, “In both origami and science, you’re discovering patterns and relationships.” He’s designed a telescope lens that folds up for shipment to space.

Lang’s origami is pushing the limits of what one can make by folding paper. At left is K2, opus 39, a polyhedron. At right is Flying Katydid, opus 495 — inspired, Lang says, by a challenge and photograph of the real insect from Brian Chan. More of Lang’s art is at www.langorigami.com.

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Robert J. Lang had a good career as a laser physicist. He worked at NASA's Jet Propulsion Laboratory. Then in 2001, he gave it all up. To fold paper.

Robert Lang had a good career as a laser physicist. He worked at NASA’s Jet Propulsion Laboratory, researching semiconductor lasers used in fiber-optic communications, before switching to a private technology firm in Silicon Valley, where he held positions such as chief scientist and vice president of research and development.

Then in 2001, he gave it all up. To fold paper.

Lang, 49, is an origami master. Paper cranes? Pshaw. Try a rattlesnake with 1,500 scales, a life-size replica of comedian Drew Carey or an American flag that was photographed for The New York Times Magazine. Lang is pushing the limits of what one can make by folding paper, but he’s also a leader in an emerging field of study called computational origami, which he boils down to this question: “How do you use rules and math to create an object of art?”

“In both origami and science, you’re discovering patterns and relationships that, in a sense, already existed before we discovered them,” Lang says. “There’s a joy of discovery and of being the first explorer in this little nook.”

He and others are using the Japanese art form to solve scientific problems. About 10 years ago, for instance, Lang collaborated with Lawrence Livermore National Laboratory to design a telescope lens that could go to space. Origami principles were ideal for the task because the lens, called the Eyeglass, needed to be big — about the size of a football field — once in space but also small enough to be shot into orbit by a rocket. A prototype demonstrated that hinged panes of glass could be used to compact the lens down to dimensions of no more than about 13 feet without degrading the optical performance. But the Eyeglass was never sent into space, for lack of funding.

Lang also has worked on computer models for folding car air bags. Simulating air-bag deployment is important because otherwise auto manufacturers would have to crash a lot of cars to determine which ones are safe — an expensive prospect.

Oxford University researchers have used origami techniques to design stents, which must be small enough for doctors to thread through a blood vessel but then pop open big enough to hold the artery or vein open.

“The things we do for fun and pleasure turn out to have practical applications, and in the case of origami, it might save a life,” Lang says.

Long paper trail

Art historians aren’t sure when origami started, but traditional designs such as cranes and boats existed in the 1700s. The craft didn’t change much until the middle of the 20th century, when Akira Yoshizawa inspired a renaissance in paper folding.

Yoshizawa, who died in 2005, developed a language of arrows and lines to show people how to fold different designs. Yoshizawa’s instructions included no words, so anyone could understand them.

There are different genres of origami so there are no “rules,” per se, but Lang mostly creates single-sheet origami without any cutting, taping or gluing.

In 2003, Lang published “Origami Design Secrets: Mathematical Methods for an Ancient Art,” a book that has become the bible for complex origami designers; he calls it his magnum opus. (He has also published seven books of folding instructions.)

While it might seem that a career as a Silicon Valley physicist would be more profitable than full-time origamist, Lang has no trouble making ends meet, with a full schedule of lectures plus book royalties, scientific commissions, art sales and commercial advertising projects, including origami creations for McDonald’s, Mitsubishi and Toyota.

Undercutting math fear

Lang isn’t the only math and science wonk enchanted by paper folding.

“I remember being 10 years old and unfolding an origami crane and looking at the crease pattern and thinking, ‘There are all these nice geometric lines and points. There’s got to be math here,’ ” recalls Tom Hull, an associate professor of mathematics at Western New England College in Springfield, Mass. “But I had no clue what it was, because I was 10.”

Today, Hull uses origami when he teaches, finding ways to tie it into to concepts in calculus, number theory, geometry and algebra. He says it’s a quick way to engage his students and to help them understand vague concepts in a visual way. In 2006, he published “Project Origami,” a book filled with activities that teachers can use in math classes.

“Kids are so afraid of math. The world is so afraid of math,” Hull says. “But with origami, they’re not thinking, ‘I’m doing this scary math thing,’ they’re just folding paper. It’s a neat way to break the barriers down.”

While most advanced origamists turn to math to fold bigger and better models, Massachusetts Institute of Technology associate professor Erik Demaine turned to origami to find more difficult geometric problems to solve. In 1996, Demaine was starting a Ph.D. in computer science at the University of Waterloo in Ontario (he was 15 at the time) and stumbled upon Lang’s work. “I thought, ‘Oh, that sounds cool. Maybe we can do something new.’ “

Now, Lang and Demaine are working together on a mathematical proof of the tree method of origami design. (Their paper is so long now that they might end up publishing it as a book.) Lang has released five versions of TreeMaker, a software program that allows origami artists to sketch stick figures and have their computer spit out a crease pattern that they can follow.

Separately, Demaine is researching the microbiological applications of origami. He suspects that the principles that govern origami might also dictate how protein molecules fold in our bodies — a process that, when it goes wrong, has been linked to illnesses such as Alzheimer’s and Parkinson’s diseases.

“That would be the endpoint, to predict what nature is doing,” Demaine says.

“Crazy idea” evolves

Demaine has three paper sculptures in the permanent collection at the Museum of Modern Art in New York, works that he created with his father, visual artist Martin Demaine. In 2003, he was awarded a MacArthur Foundation $500,000 “genius grant” for computational origami.

“It was more the recognition and acceptance that were meaningful,” Demaine says. “Computational origami was initially a very crazy idea, and yet it has so many practical applications.”

Lang, meanwhile, continues to spread the origami way. At a recent lecture at the Walters Art Museum in Baltimore, Lang showed photos of his Black Forest Cuckoo Clock, a tree frog, a Roosevelt elk and more.

“Relatively few knew I had this secret life,” says Lang of his laser physicist days. “I kept a pretty rigid separation. What’s been kind of fun is when people who I used to work with find my Web site and they say, ‘I had no idea!’ “